Preheat oven to 350 degrees. Line a 12-cup muffin tin with paper liners.

Whisk together flour, baking soda, salt, cinnamon, cardamom, and nutmeg in a bowl.

In a large mixing bowl, beat together oil, brown sugar, eggs, and vanilla until smooth. Beat in flour mixture until well combined. Gently fold in carrots, walnuts and coconut until just combined.

Divide batter evenly among muffin cups. Bake 25-30 minutes, turning pan halfway through cooking time, until a tester inserted in the middle of a cupcake comes out clean. Turn cupcakes out onto rack to cool completely.

For the Icing:

Place icing sugar in the bowl of a food processor and pulse to remove any lumps. Add remaining ingredients and process until smooth and thick. If icing is runny (as mine was on a highly humid Saturday morning), refrigerate it for an hour or so until firm enough to pipe onto the tops of the cupcakes.